Geodesic
Leibniz Algebras, Lie Racks, and Digroups
Journal of Lie theory, Tome 17 (2007) no. 1, pp. 99-114 Cet article a éte moissonné depuis la source Heldermann Verlag

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The "coquecigrue" problem for Leibniz algebras is that of finding an appropriate generalization of Lie's third theorem, that is, of finding a generalization of the notion of group such that Leibniz algebras are the corresponding tangent algebra structures. The difficulty is determining exactly what properties this generalization should have. Here we show that Lie racks, smooth left distributive structures, have Leibniz algebra structures on their tangent spaces at certain distinguished points. One way of producing racks is by conjugation in digroups, a generalization of group which is essentially due to Loday. Using semigroup theory, we show that every digroup is a product of a group and a trivial digroup.
Classification : 17A32, 20M99, 22A30
Mots-clés : Leibniz algebra, Lie rack, digroup 
@article{JLT_2007_17_1_JLT_2007_17_1_a6,
     author = {M. K. Kinyon },
     title = {Leibniz {Algebras,} {Lie} {Racks,} and {Digroups}},
     journal = {Journal of Lie theory},
     pages = {99--114},
     year = {2007},
     volume = {17},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2007_17_1_JLT_2007_17_1_a6/}
}
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M. K. Kinyon . Leibniz Algebras, Lie Racks, and Digroups. Journal of Lie theory, Tome 17 (2007) no. 1, pp. 99-114. http://geodesic.mathdoc.fr/item/JLT_2007_17_1_JLT_2007_17_1_a6/